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Papers by M. Mohrenschildt
Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334), 2000
This papers investigates the stability and control of hybrid systems. While stability is well def... more This papers investigates the stability and control of hybrid systems. While stability is well defined and studied for continuous systems, hybrid systems (mixed continuous discrete systems) pose interesting and challenging new problems. The same holds for the question of control. We model hybrid systems using hybrid automata. The notion of observability and controllability is extended to hybrid system. We present
Journal of Symbolic Computation, 1998
Computer algebra systems often have to deal with piecewise continuous functions. These are, for e... more Computer algebra systems often have to deal with piecewise continuous functions. These are, for example, the absolute value function, signum, piecewise defined functions but also functions that are the supremum or infimum of two functions. We present a new algebraic approach to these types of problems. This paper presents a normal form for a function ring containing piecewise polynomial functions of a real variable. We give a complete rule system to compute the normal form of an expression. The main result is that this normal form can be used to decide extensional equality of two piecewise functions. Also we define supremum and infimum for piecewise functions; in fact, we show that the function ring forms a lattice. Additionally, a method to solve equalities and inequalities in this function ring is presented. Finally, we give a "user interface" to the algebraic representation of the piecewise functions.
Conference on Frontiers in Education, 1998
The authors present a course project which was successfully used to teach software design princip... more The authors present a course project which was successfully used to teach software design principles to third year computer engineering students. The goal of the project is to program a robot to trace a shortest path through a maze. The students, organized in teams of five, have to follow the classical steps of software development and prepare interface, design and
34th Annual Frontiers in Education, 2004. FIE 2004., 2004
... Simple Steps Towards a Formal Specification ... theory can be made most engineers lack the ba... more ... Simple Steps Towards a Formal Specification ... theory can be made most engineers lack the background required to employ formal into an effective specification language ... The languages UML and Z use two dimensional graphical constructs to assist the composer and reader of ...
Proceedings of the 1997 international symposium on Symbolic and algebraic computation - ISSAC '97, 1997
When a computer algebra system has an assumption facility, it is possible to distinguish between ... more When a computer algebra system has an assumption facility, it is possible to distinguish between integration problems with respect to a real variable, and those with respect to a complex variable. Here, a class of integration problems is defined in which the integrand consists of compositions of continuous functions and signum functions. and integration is with respect to a real variable. Algorithms are given for evaluating such integrals.
Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301), 2002
Dynamic systems with a mix of continuous and discrete components, often called hybrid dynamic sys... more Dynamic systems with a mix of continuous and discrete components, often called hybrid dynamic systems, frequently arise in engineering applications. Since many of these applications are safety critical, it is important to use reliable methods to simulate hybrid systems.
SIGSAM Communications in Computer Algebra, 2006
Abstract Convex optimization is a branch of mathematics dealing with non-linear optimization prob... more Abstract Convex optimization is a branch of mathematics dealing with non-linear optimization problems with additional geometric structure. This area has been the focus of considerable recent research due to the fact that convex optimization problems are scalable and can be ...
ABSTRACT The notions of the Fenchel conjugate and the subdifferential of a convex function are fu... more ABSTRACT The notions of the Fenchel conjugate and the subdifferential of a convex function are fundamental in optimization. The package fenchel allows the symbolic computation of these objects for numerous convex functions defined on the real line.
A microkernel system is described that provides services for creating and extending formal langua... more A microkernel system is described that provides services for creating and extending formal languages, theories, computations, deductions, and interpretations of one theory in another. In analogy to an operating system microkernel, this microkernel is a platform for implementing multiple logics and interpretations between logics. It is intended to be the bottom layer of a mechanized mathematics system that supports the full mathematics process with the capabilities of both contemporary theorem proving systems and computer algebra systems.
ABSTRACT Wepresent a course project whichwas successfully used to teachsoftware design principles... more ABSTRACT Wepresent a course project whichwas successfully used to teachsoftware design principles to third year computer engineering students. The goal of the project is to program a robot to trace a shortest path through a maze. The students, organized in teams of #ve, have to follow the classical steps of software development and prepare interface, design and testing documents. Having a project that requires controlling a device to complete a clear task generates enthusiasm in the students and helps them to understand the principles taught in the course. 1 Introduction Computer Engineering 3VA3 is a third year course in software design taught at McMaster University. A key element of this course is an opportunitytoapply software engineering principles suchassoftware speci#cation, design and testing to systems with safety-critical and realtime requirements in a concrete project. In previous years pure software projects i.e., projects that did not involve anyhardware other than the computer, w...
Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334), 2000
This papers investigates the stability and control of hybrid systems. While stability is well def... more This papers investigates the stability and control of hybrid systems. While stability is well defined and studied for continuous systems, hybrid systems (mixed continuous discrete systems) pose interesting and challenging new problems. The same holds for the question of control. We model hybrid systems using hybrid automata. The notion of observability and controllability is extended to hybrid system. We present
Journal of Symbolic Computation, 1998
Computer algebra systems often have to deal with piecewise continuous functions. These are, for e... more Computer algebra systems often have to deal with piecewise continuous functions. These are, for example, the absolute value function, signum, piecewise defined functions but also functions that are the supremum or infimum of two functions. We present a new algebraic approach to these types of problems. This paper presents a normal form for a function ring containing piecewise polynomial functions of a real variable. We give a complete rule system to compute the normal form of an expression. The main result is that this normal form can be used to decide extensional equality of two piecewise functions. Also we define supremum and infimum for piecewise functions; in fact, we show that the function ring forms a lattice. Additionally, a method to solve equalities and inequalities in this function ring is presented. Finally, we give a "user interface" to the algebraic representation of the piecewise functions.
Conference on Frontiers in Education, 1998
The authors present a course project which was successfully used to teach software design princip... more The authors present a course project which was successfully used to teach software design principles to third year computer engineering students. The goal of the project is to program a robot to trace a shortest path through a maze. The students, organized in teams of five, have to follow the classical steps of software development and prepare interface, design and
34th Annual Frontiers in Education, 2004. FIE 2004., 2004
... Simple Steps Towards a Formal Specification ... theory can be made most engineers lack the ba... more ... Simple Steps Towards a Formal Specification ... theory can be made most engineers lack the background required to employ formal into an effective specification language ... The languages UML and Z use two dimensional graphical constructs to assist the composer and reader of ...
Proceedings of the 1997 international symposium on Symbolic and algebraic computation - ISSAC '97, 1997
When a computer algebra system has an assumption facility, it is possible to distinguish between ... more When a computer algebra system has an assumption facility, it is possible to distinguish between integration problems with respect to a real variable, and those with respect to a complex variable. Here, a class of integration problems is defined in which the integrand consists of compositions of continuous functions and signum functions. and integration is with respect to a real variable. Algorithms are given for evaluating such integrals.
Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301), 2002
Dynamic systems with a mix of continuous and discrete components, often called hybrid dynamic sys... more Dynamic systems with a mix of continuous and discrete components, often called hybrid dynamic systems, frequently arise in engineering applications. Since many of these applications are safety critical, it is important to use reliable methods to simulate hybrid systems.
SIGSAM Communications in Computer Algebra, 2006
Abstract Convex optimization is a branch of mathematics dealing with non-linear optimization prob... more Abstract Convex optimization is a branch of mathematics dealing with non-linear optimization problems with additional geometric structure. This area has been the focus of considerable recent research due to the fact that convex optimization problems are scalable and can be ...
ABSTRACT The notions of the Fenchel conjugate and the subdifferential of a convex function are fu... more ABSTRACT The notions of the Fenchel conjugate and the subdifferential of a convex function are fundamental in optimization. The package fenchel allows the symbolic computation of these objects for numerous convex functions defined on the real line.
A microkernel system is described that provides services for creating and extending formal langua... more A microkernel system is described that provides services for creating and extending formal languages, theories, computations, deductions, and interpretations of one theory in another. In analogy to an operating system microkernel, this microkernel is a platform for implementing multiple logics and interpretations between logics. It is intended to be the bottom layer of a mechanized mathematics system that supports the full mathematics process with the capabilities of both contemporary theorem proving systems and computer algebra systems.
ABSTRACT Wepresent a course project whichwas successfully used to teachsoftware design principles... more ABSTRACT Wepresent a course project whichwas successfully used to teachsoftware design principles to third year computer engineering students. The goal of the project is to program a robot to trace a shortest path through a maze. The students, organized in teams of #ve, have to follow the classical steps of software development and prepare interface, design and testing documents. Having a project that requires controlling a device to complete a clear task generates enthusiasm in the students and helps them to understand the principles taught in the course. 1 Introduction Computer Engineering 3VA3 is a third year course in software design taught at McMaster University. A key element of this course is an opportunitytoapply software engineering principles suchassoftware speci#cation, design and testing to systems with safety-critical and realtime requirements in a concrete project. In previous years pure software projects i.e., projects that did not involve anyhardware other than the computer, w...